Bio-Inspired Metaheuristic Methods for Fitting Points in CAGD

Abstract

This paper deals with a classical optimization problem, fitting 3D data points by means of curve and surface models used in Computer-Aided Geometric Design (CAGD). Our approach is based on the idea of combining traditional techniques, namely best approximation by least-squares, with Genetic Algorithms (GA) and Particle Swarm Optimization (PSO), both based on bioinspired procedures emerging from the artificial intelligence world. In this work, we focus on fitting points through free-form parametric curves and surfaces. This issue plays an important role in real problems such as construction of car bodies, ship hulls, airplane fuselage, and other free-form objects. A typical example comes from reverse engineering where free-form curves and surfaces are extracted from clouds of data points. The performance of the proposed methods is analyzed by using some examples of Bezier curves and surfaces.